A semi-algebraic approach that enables the design of inter-grid operators to optimize multigrid convergence

2008 ◽  
Vol 15 (2-3) ◽  
pp. 219-247 ◽  
Author(s):  
Pablo Navarrete Michelini ◽  
Edward J. Coyle
Keyword(s):  
Algebraic Approach ◽  
Multigrid Convergence ◽  
Grid Operators

Multilevel Algebraic Approach for Performance Analysis of Parallel Algorithms

2019 ◽  
Vol 38 (4) ◽  
pp. 817-850 ◽  
Author(s):  
Luisa D'Amore ◽  
Valeria Mele ◽  
Diego Romano ◽  
Giuliano Laccetti
Keyword(s):  
Performance Analysis ◽  
Parallel Algorithms ◽  
Algebraic Approach

scholarly journals Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Interest Rate ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Bond Pricing ◽  
Model Parameters ◽  
Time Varying ◽  
Single Factor ◽  
Bond Price ◽  
Interest Rate Models ◽  
Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

scholarly journals Transposition of European Guidelines for Energy Communities into Austrian Law: A Comparison and Discussion of Issues and Positive Aspects

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3922
Author(s):  
Bernadette Fina ◽  
Hubert Fechner
Keyword(s):  
Renewable Energy ◽  
Electricity Market ◽  
Clean Energy ◽  
Detailed Comparison ◽  
Regulatory Framework ◽  
Policy Makers ◽  
European Guidelines ◽  
Subsequent Discussion ◽  
Grid Operators ◽  
Austrian Law

The Renewable Energy Directive and the Electricity Market Directive, both parts of the Clean Energy for all Europeans Package (issued in 2019), provide supranational rules for renewable energy communities and citizen energy communities. Since national transpositions need to be completed within two years, Austria has already drafted corresponding legislation. This article aims at providing a detailed comparison of the European guidelines and the transposition into Austrian law. The comparison not only shows how, and to what extent, the European guidelines are transposed into Austrian law, but also helps to identify loopholes and barriers. The subsequent discussion of these issues as well as positive aspects of the Austrian transposition may be advantageous for legislators and policy makers worldwide in their process of designing a coherent regulatory framework. It is concluded that experts from different areas (i.e., project developers, scientists concerned with energy communities, energy suppliers and grid operators) should be closely involved in the law-making process in order to introduce different perspectives so that a consistent and supportive regulatory framework for energy communities is created.

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals Algebraic approach and Berry phase of a Hamiltonian with a general SU(1, 1) symmetry

2021 ◽  
Vol 62 (7) ◽  
pp. 071701
Author(s):  
E. Choreño ◽  
R. Valencia ◽  
D. Ojeda-Guillén
Keyword(s):  
Berry Phase ◽  
Algebraic Approach
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